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This paper presents an integrated approach to optimize for design and control of mechanical systems with random input parameters. Random parameters are represented by probability density functions. A numerical technique defining directly the representative values and the associated probabilities is implemented by modeling the stochastic parameters as generalized Wiener processes. The Monte Carlo¡s method is also implemented to deal with correlated parameters. A design and control sensitivity analysis optimization formulation is derived. A conceptual separation between time variant and time invariant design parameters is presented, this way including the design space into the control space and considering the design variables as control variables not depending on time. By using time integrals through all the derivations, the design and control problems are unified. In the optimization process we can use both types of variables simultaneously or by interdependent levels. The dynamic response is modeled via space and time finite elements, and is integrated either by at-once integration or step-by-step. The formulation is applied to a numerical example. [ABSTRACT FROM AUTHOR]